Time and Work
Math MCQs

Question :    If Janet can finish the work in 98 days and Russell can finish the same work in 103 days, then in how many days both can finish the work together?

Correct Answer  50 ⁴⁴/₂₀₁ days or 50.219 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Janet = 98 days

And, the number of days to finish the same work by Russell = 103 days

Thus, the number of days to finish the work by Janet and Russell together = ?

Here,

∵ In 98 days the work done by Janet = 1

∴ In 1 day, the work done by Janet = ¹/₉₈ part

Similarly,

∵ In 103 days the work done by Russell = 1

∴ In 1 day, the work done by Russell = ¹/₁₀₃ part

Now, in 1 day, the work done by Janet and Russell together

= In 1 day work done by Janet + In 1 day the work done by Russell

= ¹/₉₈ + ¹/₁₀₃

= ^{103 + 98}/₁₀₀₉₄

= ²⁰¹/₁₀₀₉₄ part of work

This means in 1 day, ²⁰¹/₁₀₀₉₄ part of work is done by Janet and Russell working together.

Now, the number of days required to finish ²⁰¹/₁₀₀₉₄ part of work by Janet + Russell working together = 1

∴ the number of days required to finish 1 work by Janet + Russell together

= ¹/_{²⁰¹/10094}

= 1 × ¹⁰⁰⁹⁴/₂₀₁ = ¹⁰⁰⁹⁴/₂₀₁ days

= 50 ⁴⁴/₂₀₁ days = or 50.219 days

Thus, Janet and Russell working together will finish the work in 50 ⁴⁴/₂₀₁ days = or 50.219 days Answer

Shortcut Trick to solve the problems based on time and work using formula

Case: If A can finish a work in a days, and B can finish the same work in b days,
then working together the number of days require to finish the work
= ^{a × b}/_{a + b} days.

Here given,

The number of days required to finish the work by Janet = 98 days

And the number of days required to finish the same work by Russell = 103 days

Thus, the number of days required to finish the work Janet and Russell working together = ?

Here a = 98 days

And, b = 103 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Janet and Russell working together

= ^{98 × 103}/_{98 + 103} days

= ¹⁰⁰⁹⁴/₂₀₁ days

= 50 ⁴⁴/₂₀₁ days or 50.219

Thus, Janet and Russell together will finish the work in 50 ⁴⁴/₂₀₁ days or 50.219 days Answer

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